One percent is a hundredth of a number. This concept is used when it is necessary to designate the ratio of a share to a whole. In addition, several values ​​can be compared as percentages, while necessarily indicating which integer the percentages are calculated relative to. For example, expenses are 10% higher than income or the price of train tickets has increased by 15% compared to the fares of the previous year. A percentage above 100 means that the proportion is greater than the whole, as is often the case in statistical calculations.

Interest as a financial concept - payment, the borrower to the lender for the provision of money for temporary use. In business, there is an expression "to work for interest." In this case, it is understood that the amount of remuneration depends on profit or turnover (commission). It is impossible to do without calculating interest in accounting, business, banking. To simplify the calculations, an online percentage calculator has been developed.

The calculator allows you to calculate:

• Percentage of the set value.
• Percentage of the amount (tax on actual salary).
• Percentage of the difference (VAT from ).
• And much more...

When solving problems on a percentage calculator, you need to operate with three values, one of which is unknown (a variable is calculated according to the given parameters). The calculation scenario should be selected based on the specified conditions.

Calculation examples

1. Calculate the percentage of a number

To find a number that is 25% of 1,000 rubles, you need:

• 1,000 × 25 / 100 = 250 rubles
• Or 1,000 × 0.25 = 250 rubles.

To calculate on a regular calculator, you need to multiply 1,000 by 25 and press the% button.

2. Definition of an integer (100%)

We know that 250 rubles. is 25% of some number. How to calculate it?

Let's make a simple proportion:

• 250 rub. - 25%
• Y rub. - 100 %
• Y \u003d 250 × 100 / 25 \u003d 1,000 rubles.

3. Percentage between two numbers

Suppose a profit of 800 rubles was supposed, but they received 1,040 rubles. What is the overage percentage?

The proportion will be:

• 800 rub. - 100 %
• RUB 1,040 – Y%
• Y = 1040 × 100 / 800 = 130%

Overfulfillment of the plan for profit - 30%, that is, implementation - 130%.

4. Calculation not from 100%

For example, a store with three departments is visited by 100% of customers. In the grocery department - 800 people (67%), in the department of household chemicals - 55. What percentage of buyers come to the department of household chemicals?

Proportion:

• 800 visitors - 67%
• 55 visitors - Y %
• Y = 55 × 67 / 800 = 4.6%

5. What percentage is one number less than another

The price of the goods fell from 2,000 to 1,200 rubles. By what percent did the commodity become cheaper, or by what percentage is 1,200 less than 2,000?

• 2 000 - 100 %
• 1 200 – Y%
• Y = 1200 × 100 / 2000 = 60% (60% to 1200 of 2000)
• 100% − 60% = 40% (number 1200 is 40% less than 2000)

6. By what percentage is one number greater than another

Salary increased from 5,000 to 7,500 rubles. By what percent did the salary increase? How many percent is 7,500 more than 5,000?

• 5 000 rub. - 100 %
• 7 500 rub. - Y%
• Y = 7,500 × 100 / 5,000 = 150% (in the figure 7,500 is 150% of 5,000)
• 150% - 100% = 50% (the number 7,500 is 50% greater than 5,000)

7. Increase the number by a certain percentage

The price of goods S is higher than 1,000 rubles. by 27%. What is the price of the item?

• 1 000 rub. - 100 %
• S - 100% + 27%
• S \u003d 1,000 × (100 + 27) / 100 \u003d 1,270 rubles.

The online calculator makes calculations much easier: you need to select the type of calculation, enter a number and a percentage (in the case of calculating a percentage, the second number), indicate the accuracy of the calculation, and give a command to start actions.

If you didn’t manage to understand in the lessons how to find a percentage of a number, and there is a control or EGE on your nose, don’t be discouraged. To find the percentage of one number from another or the percentage between two numbers, it is enough to learn the meaning of the concept - “percentage” and make examples to consolidate knowledge.

It is quite easy, and even vice versa. Below are solutions to typical problems.

What is a percentage?

Any number or thing can be divided into many parts. If there are 100 such conditional parts, then each share will be called a percentage.

Recording 1% is deciphered as 0.01 or a hundredth of a number. This information will make it easy to calculate 1 percent of the number, 7 percent of the number, and so on.

Basic tasks for finding a percentage

To solve problems, it is enough to understand the definition % and correctly determine the number from which this percentage is sought in the problem. Let's consider specific solutions to typical problems to make it easier for you to understand the principle of working with percentages.

Find a specified percentage of a given number

To find out the % of a given amount, you need to divide the amount by 100 parts and multiply by the specified %.

A1= A2 * P / 100, where

• A1 - calculated value;
• A2 - given initial value;
• P - percentage specified in the task.

Example: 2,000 people rest on Las Salinas beach, 40% of them are women. How to calculate the number of women vacationing on the beach?
Decision: 2000 * 40 / 100 = 800 women

Attention! If the tasks seem too easy for you - still spend 1-2 minutes on their written solution. This will strengthen the skill and refresh the acquired knowledge.

Find a number behind its percentage of another number

To find out a number if you know its percentage of another number, you need to divide the known number by the percentage and multiply by 100%. So we find out for a start 1%, and then - 100% of the desired number.

Example: Maxim's Internet income this month amounted to $600, which is 200% of the income "for his uncle" in the office. How much does Maxim earn by working "for his uncle"?
Decision: 600 / 200 * 100 = 300$

Find the percentage of one number from another

To find how much% of a number is in another, you need to multiply their fraction by 100%.

Example: Liza bought 20 chocolates at the Romashka grocery store, and Masha bought 50. What percentage of the number of Machine sweets did Liza buy at Romashka?
Decision: 20 / 50 * 100 = 40%

Find out by what percentage one number is greater than another

To find out how much % one number is greater than another, you need to take the % of the second number from the first and subtract 100%.

Example: Tonight, 15 white cars and 75 black cars drove into the gas station. What percentage of black cars drove more than white?
Decision: 75 / 15 * 100 – 100 = 400%

Carefully! The next problem will remind you of the previous one, but the principle of solving it is slightly different. Please read the terms and conditions carefully.

Find out by what percentage one number is less than another

To calculate how much% of one of the numbers is less, you need to subtract the percentage of the smaller number from the larger one from 100%.

Example: Vasya has four cars in the garage, while Anya has only one. How many percent fewer cars fit in Anya's garage?
Decision: 100 – 1/4*100 = 75%

Carefully! When solving such tasks, it is easy to confuse which number is taken as 100%. To avoid this common error, use wildcard validation.

How to increase a value by a given percentage

To increase a number by a given %, you need to perform an addition operation after you find the % of the number.
Example: I have 40 games on Steam, according to the results of the contest, I can increase them by a percentage of which is 20. How many games will I have on Steam if I win?
Decision: 40 + 20 * 40 / 100 = 40 + 8 = 48 pcs.

Carefully! Remember the need to write down the designation of the solution in pieces, meters, percentages, kilograms - such a mistake is taken seriously by inspectors.

How to decrease the value by the specified percentage

To decrease a number by a given %, you need to find the % value of the given number and perform a subtraction operation.

Example: A bear from the zoo was given 200 liters of honey for a year, and he has already eaten 10%. How many liters does the zoo have left?
Decision: 200 - 200 * 10 / 100 = 180 liters

Attention! If you deal with the same type of problems for a long time, the principle of solving them can automatically be transferred to other problems. Combine different tasks for solutions while studying learning materials.

Universal way - the method of crosses or diagonals

For smart people and smart people. There is a universal way to find how many percent is a number in any problem - the cross method. Its essence lies in the fact that dependent numbers are written opposite each other.

Then, diagonally known numbers are multiplied and divided into a diagonal pair of unknowns. For example, to find 5% of 20 rubles, you need to make a short note:

20 - 100% (the number known in the problem is always taken as 100%)
? - 5% (the number is written under the number, the percentage is written under the percentage)

If the formula is used A1= A2 * P / 100, the same value is obtained: 20 * 5 / 100 = 1 ruble

Video "How to quickly calculate percentages in your mind"

Mathematics is not just a science that lives within the walls of the school. It is used daily in household items for various calculations. Especially often you have to find percentages of a number - this is necessary when buying goods by weight, when paying taxes, when going to a restaurant. It is extremely important to be able to quickly and correctly make such calculations.

Mathematicians represent the value as a whole, i.e. it is full 100%, and some fraction of the given value is its hundredth part. Thus, a percentage is a hundredth of some total value.. For example, 1 kilogram is 100%, and half a kilogram is 50%.

It is important to know! Shares on paper are always written with the sign "%".

Shares can always be represented as decimals: 1% = 1/100 parts = 0.01, which is very convenient when calculating manually. To determine 1% of any value, always take it as 100%, then 1% will be unknown, which is 100 times less.

It is convenient to determine the percentage of a number using proportions. Let it be necessary to take and find 1 percent of the number 349, where:

Here you should be careful, because you can get confused which is which. To avoid this, you should always write fractions (%) on one side. It is best to make a proportion in a column - then it will be more convenient to determine the percentage of the number. Find x using the cross rule:

If you know the relationship between shares and decimal fractions, then it will be even easier to count, since it is enough to separate two decimal places from the end of the digit with a comma to highlight it 1%. For example, 1% of the number 248 will be equal to 2.48, and to calculate 7% from it, it will be enough to multiply the found 1% by 7 = 2.48 * 7 = 17.36.

Basic Formulas

There are several basic formulas for solving equations with fractions.

How to find a number by its fraction? If the value of X is known, which is a few fractions of Y, and it is necessary to find the value of the unknown Y, then the expression is solved using the formula:

How to find the expression of one value from another in%? If the values ​​of Y X are known, and it is necessary to find the part that makes up the number X, then this can be represented as an expression:

These three formulas are the most common when solving various equations with proportions, so it is important to remember them and learn how to quickly apply them.

Use of calculators

Modern technologies allow you not to calculate percentages of numbers on your own, using technology. You can use a regular electronic calculator with percentages. To make sure that the device is suitable, you need to find a button on it with the image of%, these are usually found among the multiplication-division actions. After that, you can start the calculations.

Good to know! The ancestor of the calculator was the adding machine, which was created by the great mathematician Blaise Pascal.

The device looked like a box with gears inside.

How to find percentage of a number? For example, a value that is 17% of the number 123. Using a calculator, you can calculate:

1. Dial 123 so that it is displayed on the scoreboard.
2. Select the multiply action (X icon).
3. Then enter 17 and click on the corresponding button (%).
4. The scoreboard will display the answer - 20.91.

This algorithm is used to find answers to any expressions with fractions and hundredths calculations. But another convenient method is to use an online calculator. To solve the problem, it is enough to go to the site of such a calculator by entering its address in the browser line or by entering a query in a search engine.

An online calculator is a website page where there are boxes where you need to enter values. Usually, in front of the window, it is written what action the calculator performs (finds% of the quantity, the quantity by%, etc.), so you need to choose the right one. It is enough to enter the values ​​in the appropriate boxes and click on the “Solve” button (“Find”, “Calculate”, etc.), the calculator will give an answer.

Useful video

Summing up

We were often told in school that mathematics would be useful to us in life. Partly it is. Integrals and limits are not useful to us in life, but we have to count money every day. Most often, the concept of interest appears in monetary transactions. Today we are with you and we will learn to find them.

What is interest?

This word comes from the English phrase Pro Centum. After reading this phrase, you probably noticed that the word cent is present there. This is where the meaning of interest comes from. As you know, a cent is one hundredth of a dollar. Therefore, 1% is one hundredth of the number.

Now many financial indicators are measured in percentages:

1. taxes;
2. shares in the business;
3. return on investment;
4. bonuses and penalties;
5. inflation.

And not only financial:

1. fertility and mortality;
2. statistics of successful and unsuccessful marriages;
3. efficiency.

Let's take a closer look at how to calculate the percentage of the amount. We will give you some examples to help you understand.

Example 1. The taxi driver worked his shift. During the day, his revenue amounted to 5 thousand rubles. He needs to give the taxi service a commission from these orders - 15%. To find out the amount that the driver must pay, you need to multiply 5 thousand by 15, and then divide by 100. We get a result equal to 750 rubles. As you may have guessed, 15% is 15 parts out of a hundred.

Now we will give you a reverse example with the same taxi driver. So, for the shift he earned 5 thousand rubles. He spent a certain part of this money on obligatory expenses:

1. taxi service commission - 750 rubles;
2. car wash - 250 rubles;
3. fuel - 1 thousand rubles.

In total, the driver has 3 thousand rubles left. Of the 5 thousand rubles earned, he takes only 3 for himself. Now our task is to calculate what part of the total revenue he can safely put in his pocket. To do this, we need to divide 3 thousand by 5 thousand. After that, the result, equal to 0.6, is multiplied by 100%. It turns out that the driver takes 60% of the total revenue into his pocket.

Example 2. Four shareholders have opened a business. After a year of hard work, he began to generate income. The partners decided to share the profits equally, that is, each will get 25% of the profits. We need to calculate how much money each of them will receive.

Let's say a business generates income of 200 thousand rubles a month. To calculate the profit of each of the shareholders, it is necessary to multiply 200 thousand by 25, and divide by 100. We get the result - 50 thousand rubles.

Example 3. Sales conversion. A sales manager offers his company's services over the phone. He made 800 calls in a month. 280 clients became interested in the company's services. To calculate the sales conversion, you need to divide 280 by 800, then multiply by 100. The result will be 35%.

Percentage Tricks

1. a field for entering a percentage;
2. a field for entering a number, the percentage of which we will find;
3. "Calculate" button.

You can easily find such a calculator on the Internet, you do not have to bother with calculations. In principle, it is logical to enjoy all the benefits of the Internet. However, in life there are situations when it is necessary to calculate the percentage of a number, but there is no calculator at hand.

You can find online calculators on the following websites:

1. calculator888.ru;
2. fin-calc.org.ua;
3. calc.by.

If you need to find 20% or 40%, multiply the sum by 0.2 and 0.4 respectively.

A very simple technique for finding percentages - division. But it can only be used with numbers that are easily divisible by 100. For example, 100 is easily divisible by 25. The result of division is four. This means that to find 25% of the amount you just need to divide it by 4. Using the same scheme, you can find 10, 20 and 50% of the amount you need.

Knowing how to calculate interest on interest will help you plan your income. For example, with a deposit with an interest rate of 10% per year, your income for 2 years will be 21%. Because in the second year, interest was already accrued on the amount accumulated during the first year. And this is 110% of the amount of the down payment.

Conclusion

In conclusion, I would like to say that knowing how to calculate the percentage of a number, help you in life. After all, they will not be able to deceive you when selling goods and when issuing wages. You are given a certain percentage of the money that you have earned. Feel free to ask your boss for pay slips. Carefully check and recalculate all payment documents, because you can be deceived. As they say: "Trust, but verify!".

The percentage shows the hundredth of the unit, which is indicated by the "%" sign. This indicator is used to indicate the proportion of something to the whole. How to calculate a percentage of a number was still known in ancient Rome. Before the decimal system was invented, calculations were made using fractions that were a multiple of 1 to 100. Octavian Augustus took a tax of one hundredth on goods that were sold at auction, and was called Centesima Rerum Venalium. Calculations using multipliers are somewhat similar to calculating percentages.

With the replacement of currency in the Middle Ages, calculations with a denominator of one hundred became more common, and from the end of the 16th century to the beginning of the 17th century, this method of calculation began to be used by everyone, based on materials that contain arithmetic calculations. According to the materials, this method was used in calculating profit and loss, interest rate, as well as the rule of three. In the seventeenth century, this form of calculation was the standard for formulating interest rates in hundredths. The concept of interest in Russia was introduced by Peter I. However, it is believed that similar calculations began to be used in the Time of Troubles, as a result of the first binding of minted coins 1 to 100, when the ruble cost 10 hryvnias, and a little later - 100 kopecks.

Sometimes two quantities are compared without comparing their values, but as a percentage. For example, the price of two goods is not compared in terms of money, but compared as a percentage of how much the price of one product exceeds the price of the other. If it is possible to determine how much one indicator is greater or less than another, then for comparison in%, it is necessary to indicate with respect to which value the percentage is calculated. Such an indication is sometimes not needed, in the case when it is said that one indicator is greater than the other by a number of percent that is greater than the indicator 100. In this case, there is one way to find the percentage, divide the difference by the smaller of the two numbers and multiply this number by 100.

How to find percentage of a number

In order to find a percentage of a number, you need to multiply this number by the number of percent and divide the resulting number by one hundred. As a rule, there are three main types of problems for calculating interest:

• Calculate the percentage of the given number. This number must be multiplied by the specified percentage, and then the result must be divided by 100.
• Determine the number given by another number and its value as a percentage of the desired number. This number must be divided by a percentage and the result multiplied by 100.
• Determine the expression of one number from another as a percentage. Divide the first number by the second and multiply the result by 100.

As a rule, in an economy where most indicators are expressed as percentages, the change in such indicators is expressed not in% of the original indicator, but in percentage points, which show the difference between the new and old values ​​​​of the indicator. For example, if the business activity index in a country increased from 50% to 51%, then its changes are calculated in the following way: (51% -50%)/50= 1/50=2%, which is 1% in percentage points.